In this project period, we have obtained data showing that inhibitory stabilized network (ISN) models describe several areas of the mouse cortex. This means that recurrent coupling is strong enough to make the excitatory neurons unstable in the absence of reactive inhibition. Together with the Brunel group, we used inference in several simple rate-based models to provide further evidence that inhibition-stabilized-network (ISN) models can describe the data. An ISN model captures responses to different stimulation strengths and the dynamics of responses simultaneously. The data and the model together provide strong evidence that cortical responses are strongly affected by recurrent excitatory-inhibitory interconnections; the data cannot be explained by intra-laminar feedforward or multi-inhibitory-population disinhibitory models. Together, this work places important constraints on the possible set of network models that can describe cortical activity. Also with the Brunel lab, we investigated how networks of spiking neurons respond to inputs, and characterized their static transfer function (i.e. how the population firing rate depends on the mean inputs to the network). This was done in two classes of models, current-based and conductance-based. Current theories make distinct predictions about the shape of this transfer function. The balanced network model predicts a linear transfer function, while the stabilized supralinear network model (SSN) can generate various types of nonlinearities. We investigated numerically and analytically the response of networks of current-based spiking neurons as a function of coupling strength. We showed that, while a linear transfer function is obtained in the strong coupling (balanced network) limit, nonlinearities appear as the coupling is decreased. We found that these nonlinearities are present both at response onset and at saturation, and systematically characterized how they are shaped by single neuron properties and network connectivity. All SSN nonlinearities can be generated, but other regimes are also present. Work in future project periods will experimentally seek to determine the operating regime used in biological cortical networks.